The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible
Annals of mathematics, Tome 170 (2009) no. 1, pp. 45-65
For a smooth manifold $M$ we define the Teichmüller space $\mathcal{T}(M)$ of all Riemannian metrics on $M$ and the Teichmüller space $\mathcal{T}^\epsilon(M)$ of $\epsilon$-pinched negatively curved metrics on $M$, where $0\leq\epsilon\leq\infty$. We prove that if $M$ is hyperbolic, the natural inclusion $\mathcal{T}^\epsilon(M)\hookrightarrow\mathcal{T}(M)$ is, in general, not homotopically trivial. In particular, $\mathcal{T}^\epsilon(M)$ is, in general, not contractible.
@article{10_4007_annals_2009_170_45,
author = {F.~Thomas Farrell and Pedro Ontaneda},
title = {The {Teichm\"uller} space of pinched negatively curved metrics on a hyperbolic manifold is not contractible},
journal = {Annals of mathematics},
pages = {45--65},
year = {2009},
volume = {170},
number = {1},
doi = {10.4007/annals.2009.170.45},
mrnumber = {2521111},
zbl = {1171.58003},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.45/}
}
TY - JOUR AU - F. Thomas Farrell AU - Pedro Ontaneda TI - The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible JO - Annals of mathematics PY - 2009 SP - 45 EP - 65 VL - 170 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.45/ DO - 10.4007/annals.2009.170.45 LA - en ID - 10_4007_annals_2009_170_45 ER -
%0 Journal Article %A F. Thomas Farrell %A Pedro Ontaneda %T The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible %J Annals of mathematics %D 2009 %P 45-65 %V 170 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.45/ %R 10.4007/annals.2009.170.45 %G en %F 10_4007_annals_2009_170_45
F. Thomas Farrell; Pedro Ontaneda. The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible. Annals of mathematics, Tome 170 (2009) no. 1, pp. 45-65. doi: 10.4007/annals.2009.170.45
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